Re: If ZFC is incomplete it can not prove anything

you say

In particular, it decides all
of its axioms AND all of its theorems as TRUE (i.e., it PROVES them,under
1st-order logic)


hahaha got you
but godel made a distinction between proven and true

true statements are independent of proof

and peter smith has admitted godel had no notion of what truth is
so tell us
what makes those axioms and theorems true
seeing true statements according to godel are independent of proof


quote

http://en.wikipedia.org/wiki/Truth#Truth_in_mathematics
In addition, from at least the time of Hilbert's program at the turn of
the twentieth century to the proof of Gödel's theorem and the development
of the Church-Turing thesis in the early part of that century, true
statements in mathematics were generally assumed to be those statements
which are provable in a formal axiomatic system.

The works of Kurt Gödel, Alan Turing, and others shook this assumption,
with the development of statements that are true but cannot be proven
within the system


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